解:$\begin{cases}\frac{x}{2}-\frac{y}{3}=1&①\\x + 4y = 16&②\end{cases}$
由$①$得:$3x - 2y = 6 ③$
$③\times2$得:$6x - 4y = 12 ④$
$② + ④$得:$x + 4y + 6x - 4y = 16 + 12$
$7x = 28$
$x = 4$
把$x = 4$代入$②$得:$4 + 4y = 16$
$4y = 16 - 4$
$4y = 12$
$y = 3$
所以方程組的解為$\begin{cases}x = 4\\y = 3\end{cases}$